| Title:
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Subclass of analytic functions related with Miller-Ross-type Poisson distribution series (English) |
| Author:
|
Frasin, Basem Aref |
| Language:
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English |
| Journal:
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Mathematica Bohemica |
| ISSN:
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0862-7959 (print) |
| ISSN:
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2464-7136 (online) |
| Volume:
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150 |
| Issue:
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3 |
| Year:
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2025 |
| Pages:
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343-357 |
| Summary lang:
|
English |
| . |
| Category:
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math |
| . |
| Summary:
|
The purpose of the present paper is to find a necessary and sufficient condition for the Miller-Ross-type Poisson distribution series to be in the class $\mathcal {P}^{\ast }(\alpha ,\beta ,\gamma )$ of analytic functions with negative coefficients. Also, we investigate several inclusion properties of the classes of Janowski type close-to-starlike functions, Janowski type close-to-convex functions and Janowski type quasi-convex functions associated with the operator $\mathbb {I}_{\theta ,\epsilon }^{s}$ defined by this distribution. Further, we consider an integral operator related to the Miller-Ross-type Poisson distribution series. Several corollaries and consequences of the main results are also considered. (English) |
| Keyword:
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analytic function |
| Keyword:
|
starlike function |
| Keyword:
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convex function |
| Keyword:
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Hadamard product |
| Keyword:
|
Miller-Ross-type Poisson distribution series |
| MSC:
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30C45 |
| DOI:
|
10.21136/MB.2024.0002-24 |
| . |
| Date available:
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2025-09-26T14:12:03Z |
| Last updated:
|
2025-09-26 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/153080 |
| . |
| Reference:
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[1] Ahmad, M., Frasin, B., Murugusundaramoorthy, G., Al-Khazaleh, A.: An application of Mittag-Leffler-type Poisson distribution on certain subclasses of analytic functions associated with conic domains.Heliyon 7 (2021), Article ID e08109, 5 pages. 10.1016/j.heliyon.2021.e08109 |
| Reference:
|
[2] Al-Hawary, T., Frasin, B. A., Yousef, F.: Coefficient estimates for certain classes of analytic functions of complex order.Afr. Mat. 29 (2018), 1265-1271. Zbl 1413.30029, MR 3869566, 10.1007/s13370-018-0623-z |
| Reference:
|
[3] ntaş, O. Altı: On the coefficients of certain analytic functions.Math. Jap. 33 (1988), 653-659. Zbl 0653.30006, MR 0972373 |
| Reference:
|
[4] ntaş, O. Altı, Irmak, H., Owa, S., Srivastava, H. M.: Coefficient bounds for some families of starlike and convex functions of complex order.Appl. Math. Lett. 20 (2007), 1218-1222. Zbl 1139.30005, MR 2384250, 10.1016/j.aml.2007.01.003 |
| Reference:
|
[5] ntaş, O. Altı, Kiliç, Ã .Ã .: Coefficient estimates for a class containing quasi-convex functions.Turk. J. Math. 42 (2018), 2819-2825. Zbl 1424.30025, MR 3866193, 10.3906/mat-1805-90 |
| Reference:
|
[6] Amourah, A., Frasin, B. A., Ahmad, M., Yousef, F.: Exploiting the Pascal distribution series and Gegenbauer polynomials to construct and study a new subclass of analytic bi-univalent functions.Symmetry 14 (2022), Article ID 147, 8 pages. 10.3390/sym14010147 |
| Reference:
|
[7] Attiya, A. A.: Some applications of Mittag-Leffler function in the unit disk.Filomat 30 (2016), 2075-2081. Zbl 1458.30006, MR 3535604, 10.2298/FIL1607075A |
| Reference:
|
[8] Bansal, D., Prajapat, J. K.: Certain geometric properties of the Mittag-Leffler functions.Complex Var. Elliptic Equ. 61 (2016), 338-350. Zbl 1336.33039, MR 3454110, 10.1080/17476933.2015.1079628 |
| Reference:
|
[9] Cho, N. E., Woo, S. Y., Owa, S.: Uniform convexity properties for hypergeometric functions.Fract. Calc. Appl. Anal. 5 (2002), 303-313. Zbl 1028.30013, MR 1922272 |
| Reference:
|
[10] El-Ashwah, R. M., Kota, W. Y.: Some condition on a Poisson distribution series to be in subclasses of univalent functions.Acta Univ. Apulensis, Math. Inform. 51 (2017), 89-103. Zbl 1413.30053, MR 3711116, 10.17114/j.aua.2017.51.08 |
| Reference:
|
[11] El-Deeb, S. M., Bulboacă, T., Dziok, J.: Pascal distribution series connected with certain subclasses of univalent functions.Kyungpook Math. J. 59 (2019), 301-314. Zbl 1435.30045, MR 3987710, 10.5666/KMJ.2019.59.2.301 |
| Reference:
|
[12] Frasin, B. A., Al-Hawary, T., Yousef, F.: Necessary and sufficient conditions for hypergeometric functions to be in a subclass of analytic functions.Afr. Mat. 30 (2019), 223-230. Zbl 1438.30042, MR 3927324, 10.1007/s13370-018-0638-5 |
| Reference:
|
[13] Frasin, B. A., Al-Hawary, T., Yousef, F.: Some properties of a linear operator involving generalized Mittag-Leffler function.Stud. Univ. Babeş-Bolyai, Math. 65 (2020), 67-75. Zbl 1513.33050, MR 4085426, 10.24193/subbmath.2020.1.06 |
| Reference:
|
[14] Frasin, B. A., Aydoğan, S. M.: Pascal distribution series for subclasses of analytic functions associated with conic domains.Afr. Mat. 32 (2021), 105-113. Zbl 1474.30075, MR 4222458, 10.1007/s13370-020-00813-1 |
| Reference:
|
[15] Frasin, B. A., Gharaibeh, M. M.: Subclass of analytic functions associated with Poisson distribution series.Afr. Mat. 31 (2020), 1167-1173. Zbl 1463.30053, MR 4154545, 10.1007/s13370-020-00788-z |
| Reference:
|
[16] Frasin, B. A., Murugusundaramoorthy, G., Aouf, M. K.: Subclasses of analytic functions associated with Mittag-Leffler-type Poisson distribution.Palest. J. Math. 11 (2022), 496-503. Zbl 1494.30025, MR 4345785 |
| Reference:
|
[17] Garg, M., Manohar, P., Kalla, S. L.: A Mittag-Leffler-type function of two variables.Integral Transforms Spec. Funct. 24 (2013), 934-944. Zbl 1292.33020, MR 3172007, 10.1080/10652469.2013.789872 |
| Reference:
|
[18] Gupta, V. P., Jain, P. K.: Certain classes of univalent functions with negative coefficients. II.Bull. Aust. Math. Soc. 15 (1976), 467-473. Zbl 0335.30010, MR 0435374, 10.1017/S0004972700022917 |
| Reference:
|
[19] Janowski, W.: Some extremal problems for certain families of analytic functions. I.Ann. Pol. Math. 28 (1973), 297-326. Zbl 0275.30009, MR 0328059, 10.4064/ap-28-3-297-326 |
| Reference:
|
[20] Joshi, S. B., Joshi, S. S., Pawar, H. H., Ritelli, D.: Connections between normalized Wright functions with families of analytic functions with negative coefficients.Analysis, München 42 (2022), 111-119. Zbl 1510.33018, MR 4415955, 10.1515/anly-2021-1027 |
| Reference:
|
[21] Kaplan, W.: Close-to-convex schlicht functions.Mich. Math. J. 1 (1952), 169-185. Zbl 0048.31101, MR 0054711, 10.1307/mmj/1028988895 |
| Reference:
|
[22] Kim, H. S., Lee, S. K.: Some classes of univalent functions.Math. Jap. 32 (1987), 781-796. Zbl 0648.30010, MR 0918290 |
| Reference:
|
[23] Kulkarni, S. R.: Some Problems Connected with Univalent Functions: Ph.D. Thesis.Shivaji University, Kolhapur (1981). |
| Reference:
|
[24] Merkes, E. P., Scott, W. T.: Starlike hypergeometric functions.Proc. Am. Math. Soc. 12 (1961), 885-888. Zbl 0102.06502, MR 143950, 10.1090/S0002-9939-1961-0143950-1 |
| Reference:
|
[25] Miller, K. S., Ross, B.: An Introduction to the Fractional Calculus and Fractional Differential Equations.John Wiley & Sons, New York (1993). Zbl 0789.26002, MR 1219954 |
| Reference:
|
[26] Mittag-Leffler, G.: Sur la nouvelle fonction $E_{\alpha}(x)$.C. R. Acad. Sci. Paris 137 (1904), 554-558 French \99999JFM99999 34.0435.01. |
| Reference:
|
[27] Murugusundaramoorthy, G., Frasin, B. A., Al-Hawary, T.: Uniformly convex spiral functions and uniformly spirallike functions associated with Pascal distribution series.Math. Bohem. 147 (2022), 407-417. Zbl 1524.30070, MR 4482314, 10.21136/MB.2021.0132-20 |
| Reference:
|
[28] Murugusundaramoorthy, G., Vijaya, K., Porwal, S.: Some inclusion results of certain subclass of analytic functions associated with Poisson distribution series.Hacet. J. Math. Stat. 45 (2016), 1101-1107. Zbl 1359.30022, MR 3585439, 10.15672/HJMS.20164513110 |
| Reference:
|
[29] Noor, K. I., Thomas, D. K.: Quasi-convex univalent functions.Int. J. Math. Math. Sci. 3 (1980), 255-266. 10.1155/S016117128000018X |
| Reference:
|
[30] Porwal, S.: An application of a Poisson distribution series on certain analytic functions.J. Complex Anal. 2014 (2014), Article ID 984135, 3 pages. Zbl 1310.30017, MR 3173344, 10.1155/2014/984135 |
| Reference:
|
[31] Reade, M. O.: On close-to-convex univalent functions.Mich. Math. J. 3 (1955), 59-62. Zbl 0070.07302, MR 0070715, 10.1307/mmj/1031710535 |
| Reference:
|
[32] Şeker, B., Eker, S. S., Çekiç, B.: On subclass of analytic functions associated with MillerRoss-type Poisson distribution series.Sahand Commun. Math. Anal. 19 (2022), 69-79. Zbl 1513.30085, 10.22130/scma.2022.551474.1091 |
| Reference:
|
[33] Shamaki, A., Frasin, B. A., Seoudy, T. M.: Subclass of analytic functions related with Pascal distribution series.J. Math. 2022 (2022), Article ID 8355285, 5 pages. MR 4392098, 10.1155/2022/8355285 |
| Reference:
|
[34] Silverman, H.: Starlike and convexity properties for hypergeometric functions.J. Math. Anal. Appl. 172 (1993), 574-581. Zbl 0774.30015, MR 1201006, 10.1006/jmaa.1993.1044 |
| Reference:
|
[35] Silverman, H., Silvia, E. M.: Subclasses of starlike functions subordinate to convex functions.Can. J. Math. 37 (1985), 48-61. Zbl 0574.30015, MR 0777038, 10.4153/CJM-1985-004-7 |
| Reference:
|
[36] Themangani, R., Porwal, S., Magesh, N.: Generalized hypergeometric distribution and its applications on univalent functions.J. Inequal. Appl. 2020 (2020), Article ID 249, 10 pages. Zbl 1503.30047, MR 4179869, 10.1186/s13660-020-02515-5 |
| Reference:
|
[37] Wiman, A.: Über die Nullstellen der Funktionen $E_{\alpha}(x)$.Acta Math. 29 (1905), 217-134 German \99999JFM99999 36.0472.01. MR 1555016, 10.1007/BF02403204 |
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